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Instability and oscillation issues originating in high-voltage direct current (HVDC) systems comprising modular multilevel converters (MMCs) are gaining increasing interest in the research community. To detect such phenomena in advance, considerable effort has been devoted recently to developing MMC models for small-signal analysis. The derivation of such models is a challenging task due to the topology and complex control structure of MMCs, which results in them having a multi-frequency response. To address this issue, scholars developed methods based on dynamic phasors and harmonic state-space modelling, which, however, require extensive pen-and-paper computations. In this paper, the periodic small-signal analysis (PAC) is adopted to determine numerically several MMCs transfer functions. Such functions can be computed between any electrical circuit node or input/output port, without the need to recast the three-phase average MMC model to derive a linear equivalent one, possibly in the DQ-frame. We show how vector fitting allows converting these functions to equivalent algebraic representations, which can be profitably used to design MMCs and study their stability following some parameter changes. To showcase this feature, we exploit one of these transfer functions to detect DC-side instability in a point-to-point HVDC system. [ABSTRACT FROM AUTHOR]

This paper considers weakly and strongly input-to-state stability (ISS) of a discrete-time time-varying delayed system with synchronous impulses and switches. By employing the uniformly asymptotically stable function and mode-dependent dwell time conditions, ISS criteria are derived using the Krasovskii and Razumikhin techniques. The time differences of the Krasovskii functionals or the Razumikhin functions can be mode-dependent and time-varying, which release constraints of some existing results. As subsequent results, we apply the derived ISS criteria to the multi-agent systems (MASs). Finally, two examples considering the quasi-consensus of MASs are given to verify the established results. [ABSTRACT FROM AUTHOR]

This paper proposes to utilize intentional time delays as part of controllers to improve the damping of electromechanical oscillations of power systems. Through stability theory, the control parameter settings for which these delays in Power System Stabilizers (PSSs) improve the small signal stability of a power system are systematically identified, including the key parameter settings for which stability regions in the parameter plane remain connected for effective operation. The paper shows that PSSs with two control channels can be effectively designed to achieve best damping characteristics for a wide range of delays. Analytical results are presented on the One-Machine Infinite-Bus (OMIB) electromechanical power system model. To demonstrate the opportunities in more realistic dynamic models, our results are then implemented via numerical analysis on the IEEE standard 14-bus system. [ABSTRACT FROM AUTHOR]

The series-paralleling technique of dc-dc converters is utilized in various domains of electrical engineering for improved power conversion. Previous studies have proposed and classified the control schemes for the series-paralleled converters. However, they have several restrictions and lack diversity. The purpose of this paper is to propose passivity-based control (PBC) for the diverse output series-parallel connection of dc-dc converters. It is proved that the output series-paralleled converters regulated by PBC are asymptotically stable. The output series-paralleled converters are numerically simulated to confirm the asymptotic stability. PBC is shown to maintain the stability of the output series-paralleled converters with diverse circuit topologies, parameters, and steady-states. The result of this paper theoretically supports the numerical and experimental considerations in the previous studies and justifies the further extension of the series-parallel connection. [ABSTRACT FROM AUTHOR]

In this paper, a fixed-time backstepping fractional-order sliding mode excitation controller (FTBFOSMEC) is proposed to enhance the performance of multimachine power system. The FTBFOSMEC is designed to achieve semi-global uniform ultimate boundedness of the multimachine power system within an upper limited convergence time irrelated to the initial operating states. The FTBFOSMEC can achieve the attractive qualities of sliding mode control with strong robustness and fast dynamic response, and the merits of backstepping control in globally asymptotic stability for parametric uncertainty. In addition, the FTBFOSMEC can avoid the singularity problem of conventional SMC. Furthermore, the nonlinear first-order filter is carried out to avoid the “explosion complexity” issue of traditional backstepping control. The fractional-order controller is designed to alleviate the chattering phenomenon of the conventional SMC. Meanwhile, the FTBFOSMEC is in a continuous description, which can further eliminate the chattering phenomenon. The Lyapunov function is taken to analyze the stabilization of the multimachine power system under the control of the FTBFOSMEC, and to estimate the upper limit of convergence time. Finally, comparative results, based on the New England 10-machine 39-bus power system, indicate that the power system under the proposed FTBFOSMEC can obtain effective, robust and superior performances compared with the existing control strategies under different operating circumstances. [ABSTRACT FROM AUTHOR]

Although the cyber-physical system stability is widely studied, scholars focus more on system stability with communication time delay. Therein, grid-connected inverters with the digital control system are regarded as one simplest and typical cyber-physical system. Meanwhile, the switching/sampling frequency of the inverter is always selected as low as possible from an efficiency viewpoint, resulting in unavoidable delay time. This delay time is apt to cause the system instability, which is more prone to severity under weak grid. To this end, this paper provides a minimum switching/sampling frequency for grid-connected inverters. Firstly, the system impedance model with equivalent delay time is constructed, which is based on padé approximate approach. This equivalent delay time consists of three parts, i.e., sampling delay time in cyber/physical level, calculation delay time in cyber level and pulsewidth modulation delay time in physical level, which reflects the cyber-physical interaction impact. Furthermore, the stability forbidden criterion is applied to make the switching/sampling frequency solving process become Hurwitz matrix identification problem through space mappings. Based on these space mappings, an adaptive step search approach is adopted to obtain the minimum switching/sampling frequency. Finally, the proposed approach can well evaluate the system stability under different frequencies through simulation and experiment. [ABSTRACT FROM AUTHOR]

Analysis of ac electrical systems can be performed via frame transformations in the time-domain or via harmonic transfer functions (HTFs) in the frequency-domain. The two approaches each have unique advantages but are hard to reconcile because the coupling effect in the frequency-domain leads to infinite dimensional HTF matrices that need to be truncated. This paper explores the relation between the two representations and shows that applying a frame transformation on the input-output signals creates a direct equivalence to a similarity transformation to the HTF matrix of the system. Under certain conditions, such similarity transformations have a diagonalizing effect which, essentially, reduces the HTF matrix order from infinity to two or one, making the matrix tractable mathematically without truncation or approximation. This theory is applied to a droop-controlled voltage source inverter as an illustrative example. A stability criterion is derived in the frequency-domain which agrees with the conventional state-space model but offers greater insights into the mechanism of instability in terms of the negative damping (non-passivity) under droop control. Therefore, the paper not only establishes a unified view in theory but also offers an effective practical tool for stability assessment. [ABSTRACT FROM AUTHOR]

This paper studies the impacts of stochastic load fluctuations, namely the fluctuation intensity and the load power variation speed, on power system dynamic voltage stability. Additionally, the trade-off relationship between the two parameters is revealed, which provides important insights regarding the potential of using energy storage to maintain voltage stability under high uncertainty. To this end, Stochastic Differential-Algebraic Equations (SDAEs) are used to model the stochastic load variation; bifurcation analysis is carried out to explain the influence of stochasticity. Numerical study and Monte Carlo simulations on the IEEE 14-bus system demonstrate that a larger fluctuation intensity or a slower load power variation speed may lead to a smaller voltage stability margin. To the best of authors’ knowledge, this work uncovers the impacts of the time evolution property of the driving parameters, i.e., the load power variation speed and its trade off effect with the fluctuation intensity on the size of the dynamic voltage stability margin. [ABSTRACT FROM AUTHOR]

This paper is concerned with the attack-resilient event-triggered controller design problem of a DC microgrid with multiple nonlinear constant power loads and intermittent denial-of-service (DoS) attacks. First, for a resource efficiency purpose, an event-triggering communication scheme is delicately devised in such a way to only invoke the data transmission over the communication line when the DoS attack is inactive. Second, via characterizing the DoS active and inactive time intervals, a new switching piecewise system model for the nonlinear DC microgrid system is presented. Third, a numerically efficient design criterion on the existence of the desired attack-resilient event-triggered controller is established. It is further shown that various performance indices including resource efficiency, attack resilience, robustness against disturbance, sampling performance of the DC microgrid system can be evaluated in a unified framework. Finally, an illustrative example is given to verify the effectiveness of the proposed control design method for the DC microgrid. [ABSTRACT FROM AUTHOR]

This paper extends the definitions of effective resistance and effective conductance to characterize the overall relation (positive coupling or antagonism) between any two disjoint sets of nodes in a signed graph. It generalizes the traditional definitions that only apply to a pair of nodes. The monotonicity and convexity properties are preserved by the extended definitions. The extended definitions provide new insights into graph Laplacian definiteness and power network stability. It is proved that the Laplacian matrix of a signed graph is positive semi-definite with only one zero eigenvalue if and only if the effective conductances between some specific pairs of node sets are positive. Also, the number of Laplacian negative eigenvalues is upper bounded by the number of negative weighted edges. In addition, new conditions for the small-disturbance angle stability, hyperbolicity, and type of power system equilibria are established, which intuitively interpret angle instability as the electrical antagonism between certain two sets of nodes in the defined active power flow graph. Moreover, a novel optimal power flow (OPF) model with effective conductance constraints is formulated, which significantly enhances power system transient stability. By the properties of extended effective conductance, the proposed OPF model admits a convex relaxation representation that achieves global optimality. [ABSTRACT FROM AUTHOR]

It is well known that the frequency synchronization of complex power networks is a prerequisite for stable operation. This paper investigates the global frequency synchronization in power networks via coordinating novel controllers on both the generator-side and the load-side. The designed controllers compute the monitored information from the generator-side and load-side simultaneously, and transmit the processed signals to steer the generators and load buses for maintaining frequency stability. In particular, the generator (load)-side buses can communicate with the load (generator)-side buses, not limited to the same side. Furthermore, nonlinear switching control protocols are proposed to analyze the frequency stability for overcoming the deficiency that the conventional linearized methods can only guarantee the local stability in or near an equilibrium state. The global stability region is rigorously proven, in which the sufficient conditions are derived for achieving global frequency synchronization of power systems. Finally, a prevailing modified Western System Coordinating Council (WSCC) 9-bus system and the widely-used IEEE 39-bus system are selected to validate the effectiveness and feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a unified framework to generalize the traditional $k$ -core decomposition method for both weighted and unweighted networks. It not only subsumes previous $k$ -core decomposition methods but provides some new ones. With the help of the definition of $n$ -th order h-index, we prove that all $k$ -core indexes can be regarded as some steady state of h-index series with $n$ going to infinity. Furthermore, all $h$ -indexes we obtain in intermediate calculation steps can be used as ranking scores to assess node importance in networks. Finally, we apply the provided new methods as well as two existing ones to four real networks and compare their performances on spreading influences ranking. [ABSTRACT FROM AUTHOR]

Sensitivity analysis is an important tool for describing power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this paper, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating sensitivities of larger systems and is consistent, within machine precision, with the function whose sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as dc exciters, by deriving and implementing the adjoint jump conditions that arise from state-dependent and time-dependent switchings. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach. This paper focuses primarily on the power system dynamics, but the approach is general and can be applied to hybrid dynamical systems in a broader range of fields. [ABSTRACT FROM AUTHOR]

This paper focuses on the small-signal stability analysis of systems modelled as differential-algebraic equations and with inclusions of delays in both differential equations and algebraic constraints. The paper considers the general case for which the characteristic equation of the system is a series of infinite terms corresponding to an infinite number of delays. The expression of such a series and the conditions for its convergence are first derived analytically. Then, the effect on small-signal stability analysis is evaluated numerically through a Chebyshev discretization of the characteristic equations. Numerical appraisals focus on hybrid control systems recast into delay algebraic-differential equations as well as a benchmark dynamic power system model with inclusion of long transmission lines. [ABSTRACT FROM AUTHOR]

The paper proposes a technique to accurately and efficiently locate periodic steady-state solutions of electric power systems. This technique is based on an enhanced version of the time-domain shooting method (TDSM) and the probe-insertion technique (PIT). The latter has been successfully applied to low-power electronic circuits but it is innovative for the study of electromechanical steady-state periodic behavior of power systems. With this aim, the paper discusses the inherent criticalities of the conventional formulation of power system models (PSMs). Then, a novel formulation is proposed to accommodate the hypotheses and mathematical requirements of the TDSM and PIT. The effectiveness and numerical efficiency of the proposed model and technique are discussed through two case studies based on the IEEE 14-bus and WSCC 9-bus systems. [ABSTRACT FROM AUTHOR]

This paper addresses the stability issue of dc distributed power systems (DPS). Impedance-based methods are effective for stability assessment of voltage-source systems and current-source systems. However, these methods may not be suitable for applications involving variation of practical parameters, loading conditions, system's structures, and operating modes. Thus, for systems that do not resemble simple voltage-source systems or current-source systems, stability assessment is much less readily performed. This paper proposes an impedance-based criterion for stability assessment of dc DPS. We first classify any converter in a dc DPS as either a bus voltage controlled converter (BVCC) or a bus current controlled converter (BCCC). As a result, a dc DPS can be represented in a general form regardless of its structure and operating mode. Then, the minor loop gain of the standard dc DPS is derived precisely using a two-port small signal model. Application of the Nyquist criterion on the derived minor loop gain gives the stability requirement for the dc DPS. This proposed criterion is applicable to dc DPSs, regardless of the control method and the connection configuration. Finally, a 480 W photovoltaic (PV) system with battery energy storage and a 200 W dc DPS, in which the source converter employs a droop control, are fabricated to validate the effectiveness of the proposed criterion. [ABSTRACT FROM AUTHOR]

This article proposes a novel distributed predefined-time sliding mode controller (DPTSMC) to gain exceptional performances of power system under input saturation. Firstly, considering the saturation of excitation input to avoid the overvoltage of the coil, an auxiliary system is taken to compensate the effect of the excitation saturation. Then, the sliding mode control (SMC) and the predefined-time stability theory are taken to devise the DPTSMC to make the power system stable in a predefined time, which has an upper limit and is directly equivalent to an adjustable parameter, thus satisfying the high requirement of the power system for expected convergence time. Meanwhile, the estimated upper bound convergence time of the power system under the proposed DPTSMC is less conservative than some existing fixed-time control strategies. Moreover, the distributed control is taken to devise the DPTSMC and the controller can receive the real-time information from the phasor measurement units (PMU). Hence, the central controller is not required and the communication network is simple, thus releasing the pressure in complicated calculation and communication, and gaining rapid and coordinated response capacity. Next, the stabilization of the power system under the DPTSMC within a predefined upper limited time is proved through the Lyapunov function. Finally, the exceptional performance of the proposed DPTSMC than the existing control methods is verified through the simulation in the IEEE 39-bus 10-machine New England power system under different operation scenarios. [ABSTRACT FROM AUTHOR]

The almost sure finite-time sliding mode control issue is investigated for Markov jump systems. The switching asynchronism between the constructed controller and considered systems is studied. The influence of time-varying delays and disturbances on systems is fully considered, and the sliding mode controller design within a finite time interval is extended to the probability framework. First, the finite time interval is divided into the reaching and the sliding motion phases, and the almost sure finite-time boundedness is analyzed in both phases. Second, the sliding mode controller gain is determined by the provided linear matrix inequality-based criteria. Finally, a numerical example and DC-DC buck converter circuit example verify the effectiveness and less conservativeness of our method. [ABSTRACT FROM AUTHOR]

Many dynamical systems, including power systems, recover from perturbations more slowly as they approach critical transitions—a phenomenon known as critical slowing down. If the system is stochastically forced, autocorrelation and variance in time-series data from the system often increase before the transition, potentially providing an early warning of coming danger. In some cases, these statistical patterns are sufficiently strong, and occur sufficiently far from the transition, that they can be used to predict the distance between the current operating state and the critical point. In other cases CSD comes too late to be a good indicator. In order to better understand the extent to which CSD can be used as an indicator of proximity to bifurcation in power systems, this paper derives autocorrelation functions for three small power system models, using the stochastic differential algebraic equations (SDAE) associated with each. The analytical results, along with numerical results from a larger system, show that, although CSD does occur in power systems, its signs sometimes appear only when the system is very close to transition. On the other hand, the variance in voltage magnitudes consistently shows up as a good early warning of voltage collapse. [ABSTRACT FROM AUTHOR]

The increasing use of power electronics converters to integrate renewable energy sources has been a subject of concern due to the resonance oscillatory phenomena caused by their interaction with poorly damped AC networks. Early studies are focused on assessing the controller influence of a single converter connected to simple networks, and they are no longer representative for existing systems. Lately, studies of multi-infeed grid-connected converters are of particular interest, and their main aim is to apply traditional criteria and identify their difficulties in the stability assessment. An extension of traditional criteria is commonly proposed as a result of these analysis, but they can be burdensome for large and complex power systems. The present work addresses this issue by proposing a simple criterion to assess the stability of large power systems with high-penetration of power converters. The criterion has its origin in the mode analysis and positive-net damping stability criteria, and it addresses the stability in the frequency domain by studying the eigenvalues magnitude and real component of dynamic models in the admittance matrix form. Its effectiveness is tested in two case studies developed in Matlab/Simulink which compare it with traditional criteria, proving its simplicity. [ABSTRACT FROM AUTHOR]

This study proposes a new application for delay-dependent stability analysis of a shipboard microgrid system. Gain and phase margin values are taken into consideration in delay dependent stability analysis. Since such systems are prone to unwanted frequency oscillations against load disturbances and randomness of renewable resources, a virtual gain and phase margin tester has been incorporated into the system to achieve the desired stabilization specification. In this way, it is considered that the system provides the desired dynamic characteristics (e.g. less oscillation, early damping, etc.) in determining the time delay margin. Firstly, the time delay margin values are obtained and their accuracy in the terms of desired gain and phase margin values are investigated. Then, the accuracy of the time delay margin values obtained by using the real data of renewable energy sources and loads in the shipboard microgrid system is shown in the study. Finally, a real-time hardware-in-the-loop (HIL) simulation based on OPAL-RT is accomplished to affirm the applicability of the suggested method, from a systemic perspective, for the load frequency control problem in the shipboard microgrid. [ABSTRACT FROM AUTHOR]

As large-scale power systems are more and more closely integrated with remote transmission technologies, they are also affected by malicious factors in the cyber and physical layers when bringing convenience. In this article, we propose a novel adaptive event-triggered strategy and apply to the multi-area power system to deal with the load frequency control (LFC) problem with network-induced delay and stochastic sensor faults based on the discrete-time sliding mode control (DSMC) technique. Compared with existing event-triggered strategies, the proposed event-triggered strategy dynamically adjusts the threshold according to system state fluctuations, which can improve the system’s tolerance for sensor faults and reduce the number of transmitted packets. Firstly, a dynamic LFC model combining network-induced delay, sensor faults, adaptive event-triggered strategy and DSMC is proposed by using the analysis method of time-delay system. Then we devise an appropriate discrete-time sliding surface for each subsystem in the networked power systems. The Lyapunov stability theory is used to analyze the asymptotic stability and robustness of each subsystem, and the decentralized controller design method is derived. Finally, some simulation examples are introduced to confirm the effectiveness of the proposed adaptive event-triggered DSMC approach. [ABSTRACT FROM AUTHOR]

In this note, it is shown that the Lyapunov function-based analyses done in the above-titled article to design a backstepping sliding mode controller contain some drawbacks. These drawbacks include ignoring some terms in simplification of time-derivative of the considered Lyapunov functions, which do not vanish in a finite-time. Moreover, by presenting a counterexample, it is revealed that the finite-time convergence of the error signals cannot be necessarily concluded from a Lyapunov function-based inequality used in the aforementioned article. [ABSTRACT FROM AUTHOR]

Electric power systems subjected to large and/or unexpected disturbances can become unstable and suffer from system separations and cascading outages. A major objective of smart-grid development is to maintain power system stability under high-penetration of renewable energy. Critical system separations (due to faults cleared immediately after the critical clearing time) have important applications in transient stability analysis and relay setting, and in devising corrective measures to efficiently reduce the detrimental impacts of large disturbances. Such system separations have practical physical consequences. As the main result, an upper bound on the number of possible critical system separations is derived for the power system with $n$ generators. The analytical results are illustrated in the last section, by using the IEEE power system test cases with 9 and 57 buses, respectively, and an efficient numerical scheme is described to compute different system separations. [ABSTRACT FROM AUTHOR]

The Holomorphic Embedding Loadflow Method is extended here from AC to DC-based systems. Through an appropriate embedding technique, the method is shown to extend naturally to DC power transmission systems, preserving all the constructive and deterministic properties that allow it to obtain the white branch solution in an unequivocal way. Its applications extend to nascent meshed HVDC networks and also to power distribution systems in more-electric vehicles, ships, aircraft, and spacecraft. In these latter areas, it is shown how the method can cleanly accommodate the higher-order nonlinearities that characterize the I-V curves of many devices. The case of a photovoltaic array feeding a constant-power load is given as an example. The extension to the general problem of finding DC operating points in electronics is also discussed, and exemplified on the diode model. [ABSTRACT FROM AUTHOR]

This work studies the impact on power system dynamics of wind energy conversion systems based on permanent magnet synchronous generators when they perform ancillary services. The ability of modern variable-speed wind turbines to rapidly modify its active and reactive power is exploited in order to provide additional support to the power grid and enhance the overall stability of the system. A set of control loops are incorporated to the wind farm in order to achieve three supporting tasks: short-term frequency regulation, oscillation damping and voltage regulation. The analysis contemplates the effects of different loading conditions, measurement/communication time delays and control loop gains. Bifurcation diagrams, eigenvalue analysis and nonlinear time-domain simulations are used to assess the power system dynamics. The main contribution of this work is the assessment of wind farm ancillary services on the bifurcation structure of the power system. [ABSTRACT FROM AUTHOR]